A Numerical Method for Hedging Bermudan Options under Model Uncertainty

Model uncertainty has recently been receiving more attention than risk. This study proposes an effective computational framework to derive optimal strategies for obtaining the upper and lower bounds of Bermudan-style options in the presence of model uncertainty. The optimal hedging strategy under model uncertainty can be formulated as a solution of a minimax problem. We employ approximate dynamic programming and propose an algorithm for effectively solving the minimax problem. This study considers a geometric Brownian motion and an exponential generalized hyperbolic Lévy process as reference models. To take model uncertainty into consideration, we consider a set of equivalent probability measures via an Esscher or a class-preserving transform. Using numerical examples, we discuss the effects of model uncertainty on the size of tracking errors, the hedge portfolio, the possibility of early exercise and positions of options. In addition to investors’ optimal strategies, the study examines Nature’s optimal choice for equivalent probability measures. We find several notable phenomena that occur because of the existence of model uncertainty. We further examine the effects of different types of model uncertainty on option values and optimal hedging strategies.